📌 Section 1 is Logical reasoning specially designed for CAT
SET 1 — 🔍 CAT Level
Eight persons, A through H, were standing along a circular track, not necessarily in the same order, such that the distance along the track between any two persons standing adjacent to each other was exactly 1 km. At exactly 9:00 AM, all of them started walking along the track in the clockwise direction. However, four of them started walking at a speed of 1 km/h, while the other four started walking at a speed of 3 km/h.
The following information is known about their relative positions along the track at exactly 10:00 AM, as they were walking:
No two persons were at the same position.
G was immediately behind D, while E was diametrically opposite C.
B was not immediately behind H, while F was diametrically opposite A.
The following information is known about their relative positions along the track at exactly 11:00 AM, as they were walking:
Neither F nor B was either immediately ahead of or immediately behind H.
E was either immediately ahead of or immediately behind D.
Question 1
What is the difference between the number of Red pens with D and the number of Black pens with B?
Question 2
The difference between the total number of pens with any pair of persons is at most ______.
Question 3
One of the five persons gave a certain number of pens of exactly one colour to another of the five persons. After this, the person who gave the pens had an equal number of Red and Black pens with him; and the same was the case with the person who received the pens.
What is the total number of pens with these two persons?
Question 4
One of the five persons gave a certain number of pens of exactly one colour to one other person. After this, the person who gave the pens had an equal number of Red and Black pens with him; and the same was the case with the person who received the pens.
What is the maximum possible number of pens with any of these two persons after this?
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✅ Answers & Explanations
Since all 8 people are initially 1 km apart on an 8 km circular track, we can represent the track by positions 0–7.
Using the conditions at 10:00 AM and 11:00 AM, the only arrangement consistent with all the information gives the following speeds:
3 km/h: A, B, D, F
1 km/h: C, E, G, H
The clockwise arrangements are:
9:00 AM:
H → F → C → D → G → A → E → B → H
10:00 AM:
A → H → B → C → F → G → D → E → A
11:00 AM:
E → D → H → A → C → B → G → F → E
12 noon:
B → E → F → H → D → C → A → G → B
From this:
1️⃣ Who was immediately ahead of B at 9:00 AM?
At 9 AM:
E → B → H
So the person immediately ahead of B is H.
Answer: A — H ✅
2️⃣ At 10:00 AM, who was immediately behind E?
At 10 AM:
G → D → E → A
Hence D is immediately behind E.
Answer: C — D ✅
3️⃣ At 12 noon, who was immediately ahead of A?
At 12 noon:
C → A → G
Therefore:
Answer: A — G ✅
4️⃣ At which time will C be immediately ahead of B?
Checking the given times:
1 PM: B and C are not adjacent in the required order.
2 PM: B → C ✅
3 PM: C → B, so C is behind B.
4 PM: They are not adjacent.
Answer: D — 2:00 PM ✅
✅ Final Answers
1️⃣ H — Option A
2️⃣ D — Option C
3️⃣ G — Option A
4️⃣ 2:00 PM — Option D
⚡ Brain teasers are not just about getting the right answer — they train you to think differently under pressure.
Stay consistent with your daily practice, challenge your assumptions, and keep sharpening your reasoning skills.
See you in tomorrow’s challenge!